11) $2x^4 - 16x^5y$
12) $18u^2v + 10$
13) $56a^2b + 63ab + 21$
14) $42y^2x^5 + 54y^2x^4 + 6y^2$
15) $30 + 24b^3 + 36a^2b^2$
16) $-54xy + 12x^2 - 6x$

Question

Accepted Answer

Let's solve each problem by factoring out the greatest common factor (GCF):

### Problem 11: $2x^4 - 16x^5y$
# Explanation:
## Step1: Find GCF of coefficients and variables
The GCF of 2 and 16 is 2. For the variables, the GCF of $x^4$ and $x^5$ is $x^4$.
## Step2: Factor out the GCF
$2x^4 - 16x^5y = 2x^4(1 - 8xy)$
# Answer:
$2x^4(1 - 8xy)$

### Problem 12: $18u^2v + 10$
# Explanation:
## Step1: Find GCF of 18 and 10
The GCF of 18 and 10 is 2.
## Step2: Factor out the GCF
$18u^2v + 10 = 2(9u^2v + 5)$
# Answer:
$2(9u^2v + 5)$

### Problem 13: $56a^2b + 63ab + 21$
# Explanation:
## Step1: Find GCF of 56, 63, and 21
The GCF of 56, 63, and 21 is 7.
## Step2: Factor out the GCF
$56a^2b + 63ab + 21 = 7(8a^2b + 9ab + 3)$
# Answer:
$7(8a^2b + 9ab + 3)$

### Problem 14: $42y^2x^5 + 54y^2x^4 + 6y^2$
# Explanation:
## Step1: Find GCF of 42, 54, and 6
The GCF of 42, 54, and 6 is 6. For the variables, the GCF of $y^2x^5$, $y^2x^4$, and $y^2$ is $y^2$.
## Step2: Factor out the GCF
$42y^2x^5 + 54y^2x^4 + 6y^2 = 6y^2(7x^5 + 9x^4 + 1)$
# Answer:
$6y^2(7x^5 + 9x^4 + 1)$

### Problem 15: $30 + 24b^3 + 36a^2b^2$
# Explanation:
## Step1: Find GCF of 30, 24, and 36
The GCF of 30, 24, and 36 is 6.
## Step2: Factor out the GCF
$30 + 24b^3 + 36a^2b^2 = 6(5 + 4b^3 + 6a^2b^2)$
# Answer:
$6(5 + 4b^3 + 6a^2b^2)$

### Problem 16: $-54xy + 12x^2 - 6x$
# Explanation:
## Step1: Find GCF of -54, 12, and -6
The GCF of -54, 12, and -6 is -6 (or 6, but factoring out -6 makes the first term positive).
## Step2: Factor out the GCF
$-54xy + 12x^2 - 6x = -6x(9y - 2x + 1)$ (or $6x(-9y + 2x - 1)$, but factoring out -6x is more standard to make the first term in the parentheses positive)
# Answer:
$-6x(9y - 2x + 1)$

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QUESTION IMAGE

Question

Explanation:

Problem 11: \(2x^4 - 16x^5y\)

Step1: Find GCF of coefficients and variables

Step2: Factor out the GCF

Step1: Find GCF of 18 and 10

Step2: Factor out the GCF

Step1: Find GCF of 56, 63, and 21

Step2: Factor out the GCF

Answer:

Problem 12: \(18u^2v + 10\)